Page 479 - Handbook of Biomechatronics

Bioinspired and Biomimetic Micro-Robotics for Therapeutic Applications 473

2.2.4 Conceptual Optimization Studies on Swimming Microrobots
The hydrodynamic efficiency for micro-swimmers is conventionally
defined for the relation between forward thrust and forward motion of
the robot, but we know by observation that this is purely based on the
assumption of perfect symmetry for geometry and for induced flow field.
It is also known that any aberration of surface morphology, geometric
imperfections, the presence of nearby boundaries, or a nonhomogeneous
wave pattern is enough to break this symmetry, and even sperm cells may
exhibit three-dimensional (3D) trajectories (Corkidi et al., 2008). Thus,
to abide by the conservation of energy, the efficiency definition should
be revisited to include full 6-DOF motion. This is imperative as, in robotics,
researchers are also striving to supply the power, not in abundance or short-
age but in the right amount and control the motion with high accuracy. The
total rigid-body motion may not be a concern for some applications; how-
ever, if the robot has to be steered toward a predefined target within a maze
of ducts and intersections than, from a robotics and medical standpoint, one
needs to have an idea of what will happen with the power supplied to the
system. The ultimate efficiency could be defined as the ratio of power drain
on the entire micro-swimmer, P viscous-loss (W), to the total power supplied,
P input (W), and this will deliver yet another dimensionless number:

P viscous loss
η ¼ (12)
P input
The micro-swimmer being sought after is the fastest and the most robust one
with the minimum energy requirement. Earliest studies solely focused on
the fluid resistance as it dominates the overall swimming performance; how-
ever, some recent ones do take the overall system performance into account.
However the micro-swimmer is actuated, the goal is to tow a cargo on
which the largest portion of the input power is dissipated by means of viscous
friction. Thus, the first question is to ask what the optimum head geometry
should be to give the minimum hydrodynamic drag. The earliest answer was
given by Bourot (1974), and it is not a perfect sphere as one might first think
but more like the shape of a rugby ball with a numerically tuned aspect ratio;
very close to the shape presented in Fig. 1.
Next question should be what the overall geometry of the swimmer
should be. There are several optimization studies on the most efficient geo-
metric combination of the head (cargo) and the tail (flagellum) from the
point of view of hydrodynamics. These studies mostly carried out in